Geometry Calculators
Circle Area Calculator
Calculate the area of a circle using A = πr². Enter the radius or diameter and get the exact area (as a multiple of π) plus the decimal approximation, with full step-by-step work.
Circumference Calculator
Calculate the circumference of a circle using C = 2πr or C = πd. Enter the radius or diameter and get the exact circumference (as a multiple of π) plus a decimal result with step-by-step work shown.
Cylinder Volume Calculator
Calculate the volume, lateral surface area, and total surface area of a cylinder from its radius and height. Enter the radius or diameter and see full step-by-step solutions using V = πr²h.
Distance Between Two Points Calculator
Find the straight-line distance between any two coordinate points using the distance formula. Enter x and y for each point to get step-by-step work, a plotted diagram, and the midpoint.
Pythagorean Theorem Calculator
Enter any two sides of a right triangle and find the missing side instantly. Step-by-step work shows every squaring, adding, and square root operation using your exact values.
Rectangle Area Calculator
Calculate the area, perimeter, and diagonal of any rectangle or square. Enter length and width — or just one side for a square — and get instant results with step-by-step work and formulas.
Triangle Area Calculator
Calculate the area of a triangle using A = ½bh. Enter the base and height to see full step-by-step work with your values. Also covers Heron's formula for when all three side lengths are known.
Geometry is the branch of mathematics that deals with shapes, sizes, and the properties of space. Each of the 7+ calculators below shows you every step of the solution using your numbers, then explains the general method with worked examples.
Available Geometry Calculators
- Pythagorean Theorem Calculator — find the missing side of a right triangle given any two sides
- Circle Area Calculator — calculate the area of a circle from its radius or diameter
- Circumference Calculator — find the circumference (perimeter) of a circle
- Triangle Area Calculator — find the area of any triangle using base and height
- Rectangle Area Calculator — find the area and perimeter of a rectangle or square
- Cylinder Volume Calculator — find the volume and surface area of a cylinder
- Distance Between Two Points Calculator — find the straight-line distance between two coordinates
Geometry Reference Guide
Every geometry problem starts with a formula. Here is a quick reference for the most common shapes, with examples worked out step by step.
Right Triangles and the Pythagorean Theorem
A right triangle has one 90° angle. The two shorter sides are called legs (labeled $a$ and $b$) and the longest side — opposite the right angle — is the hypotenuse (labeled $c$).
The Pythagorean theorem states:
$$a^2 + b^2 = c^2$$Example: A triangle has legs $a = 3$ and $b = 4$. Find the hypotenuse.
$$c^2 = 3^2 + 4^2 = 9 + 16 = 25$$ $$c = \sqrt{25} = 5$$You can also solve for a leg if the hypotenuse is known:
$$a = \sqrt{c^2 - b^2}$$Circles
Two key measurements describe a circle:
- Radius ($r$) — the distance from the center to the edge
- Diameter ($d$) — the distance straight across, equal to $2r$
Area — the space inside the circle:
$$A = \pi r^2$$Circumference — the distance around the circle:
$$C = 2\pi r = \pi d$$Example: A circle has a radius of 5.
$$A = \pi \times 5^2 = 25\pi \approx 78.54$$ $$C = 2\pi \times 5 = 10\pi \approx 31.42$$Triangles
The area of any triangle is half the product of its base and height (where height is perpendicular to the base):
$$A = \frac{1}{2} \times b \times h$$Example: A triangle has a base of 10 and a height of 6.
$$A = \frac{1}{2} \times 10 \times 6 = 30$$Rectangles and Squares
A rectangle has two pairs of equal sides called length ($l$) and width ($w$).
$$\text{Area} = l \times w$$ $$\text{Perimeter} = 2l + 2w$$A square is a rectangle where $l = w$, so:
$$\text{Area} = s^2 \qquad \text{Perimeter} = 4s$$Example: A rectangle is 8 wide and 3 tall.
$$A = 8 \times 3 = 24 \qquad P = 2(8) + 2(3) = 22$$Cylinders
A cylinder has a circular base with radius $r$ and a height $h$.
$$\text{Volume} = \pi r^2 h$$ $$\text{Lateral Surface Area} = 2\pi r h$$ $$\text{Total Surface Area} = 2\pi r h + 2\pi r^2$$Example: A cylinder with radius 3 and height 7.
$$V = \pi \times 3^2 \times 7 = 63\pi \approx 197.92$$ $$\text{Total SA} = 2\pi(3)(7) + 2\pi(3^2) = 42\pi + 18\pi = 60\pi \approx 188.50$$Distance Between Two Points
The straight-line distance between points $(x_1, y_1)$ and $(x_2, y_2)$ comes from the Pythagorean theorem:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$Example: Find the distance between $(1, 2)$ and $(4, 6)$.
$$d = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$$Frequently Asked Questions
What is $\pi$ (pi)?
Pi ($\pi$) is the ratio of a circle's circumference to its diameter. It is irrational — its decimal form never ends or repeats. For calculations, use $\pi \approx 3.14159$.
What is the difference between area and perimeter?
Area measures the two-dimensional space inside a shape, expressed in square units (cm², ft², etc.). Perimeter (or circumference for circles) measures the distance around the outside, expressed in linear units.
What is volume?
Volume measures the three-dimensional space a solid occupies, expressed in cubic units (cm³, in³, etc.).
Does the Pythagorean theorem work for all triangles?
No — only right triangles. For other triangles, use the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $C$ is the angle opposite side $c$.